Optimal IOL shape factors for human eyes

ABSTRACT

The present invention provides an ophthalmic lens (e.g., an intraocular lens) having an optic with an anterior surface and a posterior surface, which exhibits a shape factor (defined as a ratio of the sum of the anterior and posterior curvatures to the difference of such curvatures) in a range of about −0.5 to about 4. In a related aspect, the shape factor of the optic lies in a range of about 0 to about 2. The above shape factors give rise to a plurality of different lens shapes, such as concave-convex, plano-convex and plano-concave.

RELATED APPLICATION

The present application claims priority to U.S. Provisional PatentApplication Ser. No. 60/668,520 entitled “Intraocular Lens,” filed onApr. 5, 2005, which is herein incorporated by reference.

A U.S. patent application entitled, “Intraocular Lens,” assigned to theassignee of the present application, and filed concurrently herewith, isherein also incorporated by reference.

BACKGROUND

The present invention relates generally to ophthalmic lenses, and moreparticularly, to intraocular lenses (IOLs) having optimal shape factors.

Intraocular lenses are routinely implanted in patients' eyes duringcataract surgery to replace the clouded natural lens. The post-operativeperformance of such IOLs, however, can be degraded due to a variety offactors. For example, aberrations introduced as a result of misalignmentof the implanted IOL relative to the cornea, and/or the inherentaberrations of the eye, can adversely affect the lens's opticalperformance.

Accordingly, there is a need for improved IOLs that can provide a morerobust optical performance.

SUMMARY

In one aspect, the present invention provides an ophthalmic lens (e.g.,an intraocular lens) having an optic with an anterior surface and aposterior surface. The optic exhibits a shape factor in a range of about−0.5 to about 4. In a related aspect, the shape factor of the optic liesin a range of about 0 to about 2. The above shape factors give rise to aplurality of different lens shapes, such as, bi-convex, plano-convex,plano-concave and convex-concave.

In another aspect, the optic is formed of a biocompatible polymericmaterial. By way of example, the optic can be formed of a soft acrylicpolymeric material. Other examples of suitable materials include,without limitation, hydrogel and silicone materials.

In another aspect, at least one surface of the optic can becharacterized by an aspheric base profile (i.e., a base profile thatexhibits deviations from sphericity). By way of example, the baseprofile can be characterized by a conic constant in a range of about −73to about −27.

In a related aspect, the aspheric profile of the lens surface can bedefined in accordance with the following relation:$z = \frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}}$wherein,

c denotes the curvature of the surface at its apex (at its intersectionwith the optical axis),

r denotes the radial distance from the optical axis, and

k denotes the conic constant,

wherein

c can be, e.g., in a range of about 0.0152 mm⁻¹ to about 0.0659 mm⁻¹,

r can be, e.g., in a range of about 0 to about 5, and

k can be, e.g., in a range of about −1162 to about −19 (e.g., in a rangeof about −73 to about −27).

In a related aspect, the optic of the above lens can have a shape factorin a range of about 0 to about 2.

In some embodiments in which one or more surfaces of the ophthalmic lensexhibit asphericity, the shape factor of the lens (e.g., an IOL) can beselected as a function of that asphericity so as to optimize the lens'soptical performance. By way of example, in one aspect, the inventionprovides an ophthalmic lens having an optic with an anterior surface anda posterior surface, where at least one of the surfaces exhibits anashperical profile characterized by a conic constant in a range of about−73 to about −27. The optic exhibits a shape factor in a range of about−0.5 to about 4.

In a related aspect, an ophthalmic lens having an optic with a shapefactor in a range of about 0 to about 2 includes at least one asphericalsurface characterized by a conic constant in a range of about −73 toabout −27.

In other aspects, an intraocular lens adapted for implantation in an eyehaving a corneal radius equal to or less than about 7.1 mm is disclosed,which includes an optic having an anterior surface and a posteriorsurface. The optic exhibits a shape factor in a range of about −0.5 toabout 4. In a related aspect, the optic exhibits a shape factor in arange of about +0.5 to about 4, or in a range of about 1 to about 3.

In another aspect, the invention provides an intraocular lens adaptedfor implantation in an eye having a corneal radius in a range of about7.1 mm to about 8.6 mm, which includes an optic having an anteriorsurface and a posterior surface. The optic exhibits a shape factor in arange of about 0 to about 3. In a related aspect, the optic exhibits ashape factor in a range of about +0.5 to about 3, or in a range of about1 to about 2.

In another aspect, an intraocular lens adapted for implantation in aneye having a corneal radius equal to or greater than about 8.6 isdisclosed, which includes an optic having an anterior surface and aposterior surface. The optic exhibits a shape factor in a range of about0.5 to about 2. In a related aspect, the optic exhibits a shape factorin a range of about 1 to about 2.

In another aspect, the invention provides an intraocular lens adaptedfor implantation in an eye having an axial length equal to or less thanabout 22 mm, which includes an optic having an anterior surface and aposterior surface. The optic can have a shape factor in a range of about0 to about 2, or in a range of about 0.5 to about 2.

In other aspects, the invention discloses methods for selecting anophthalmic lens for implantation in a patient's eye based on one or moreocular biometric parameters of the patient. For example, a method ofcorrecting vision is disclosed that includes selecting an IOL, whichcomprises an optic exhibiting a shape factor in a range of about −0.5 toabout 4 (or in a range of about +0.5 to about 4), for implantation in aneye having a corneal radius that is equal to or less than about 7.1 mm.

In another aspect, a method of correcting vision is disclosed thatincludes selecting an IOL, which comprises an optic exhibiting a shapefactor in a range of about 0 to about 3 (or in a range of about 0.5 toabout 3), for implantation in an eye having a corneal radius in a rangeof about 7.1 mm to about 8.6 mm.

In yet another aspect, a method of correcting vision is disclosed thatincludes selecting an IOL, which comprises an optic exhibiting a shapefactor in a range of about 0.5 to about 2, for implantation in an eyehaving a corneal radius that is equal to or greater than about 8.6 mm.

In another aspect, a method of corrected vision is disclosed thatincludes selecting an IOL, which comprises an optic exhibiting a shapefactor in a range of about 0 to about 2 (or in a range of about 0.5 toabout 2), for implantation in an eye having an axial length equal to orless than about 22 mm.

In another aspect, a method of designing an ophthalmic lens is disclosedthat includes defining an error function, which is indicative ofvariability in performance of a lens in a patient population, based onestimated variability in one or more biometric parameters associatedwith that population, and selecting a shape factor for the lens thatreduces the error function relative to a reference value. In a relatedaspect, the error function can further include an estimated error inoptical power correction provided by the lens and/or an estimatedaberration error.

In a related aspect, the error function (RxError) can be defined inaccordance with the following relation:${RxError} = \sqrt{{\Delta\quad{Biometric}^{2}} + {\Delta\quad{IOLPower}^{2}} + {\Delta\quad{Aberration}^{2}}}$

wherein,

ΔBiometric denotes variability due to biometric data errors,

ΔIOLPower denotes variability due to optical power correction errors,and

ΔAberration denotes variability due to aberration contributions.

In another aspect, the ΔBiometric can be defined in accordance with thefollowing relation:ΔBiometric=√{square root over (Δk ² +ΔAL ² +ΔACD ²)}

wherein,

Δk denotes error in keratometric measurements,

ΔAL denotes error in axial length measurements, and

ΔACD denotes error in anterior chamber depth measurements.

In another aspect, the ΔAberration can be defined in accordance with thefollowing relation:ΔAberration=√{square root over (ΔAstig² +ΔSA ²+ΔOther²)}

wherein,

ΔAstig represents variability due to astigmatic aberration,

ΔSA represents variability due to spherical aberration, and

ΔOther represents variability due to other aberrations.

In a further aspect, the ΔIOLPower can be defined in accordance with thefollowing relation:ΔIOLPower=√{square root over (ΔIOLStep² +ΔIOLTol² +ΔELP ²)}

wherein,

-   -   ΔIOLStep represents variability caused by difference between a        power correction provided by the lens and a power correction        needed by a patient,    -   ΔIOLTol represents manufacturing power tolerance, and    -   ΔELP represents variability in a shift of the lens effective        position within the eye.

Further understanding of the invention can be obtained by reference tothe following detailed description, in conjunction with the associateddrawings, which are discussed briefly below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view of an IOL in accordance with oneembodiment of the invention,

FIG. 2 presents simulated magnitude of different aberration types(spherical, defocus, coma and astigmatic aberrations) exhibited by anIOL as a function of its shape factor for a 1.5 mm decentration,

FIG. 3 presents simulation results for aberrations exhibited by an IOLdue to tilt as a function of the IOL's shape factor,

FIG. 4A presents graphically calculated spherical aberration exhibitedby a model eye characterized by an average anterior chamber depth inwhich an IOL is incorporated, as a function of the IOL's shape factor,

FIG. 4B presents graphically calculated MTFs at 50 lp/mm and 100 lp/mmfor a model eye characterized by an average anterior chamber depth inwhich an IOL is incorporated, as a function of the IOL's shape factor,

FIG. 5A depicts simulated MTFs at 50 lp/mm and 100 lp/mm for a model eyecharacterized by a small anterior chamber depth in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 5B depicts simulated spherical aberration exhibited by a model eyecharacterized by a small anterior chamber depth in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 6A depicts simulated spherical aberration exhibited by a model eyecharacterized by a large anterior chamber depth in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 6B depicts simulated MTFs at 50 lp/mm and 100 lp/mm for a model eyecharacterized by a large anterior chamber depth in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 7A depicts graphically simulated spherical aberrations exhibited bya plurality of model eyes having different corneal asphericities inwhich an IOL is incorporated, as a function of the IOL's shape factor,

FIG. 7B depicts graphically simulated MTF as 50 lp/mm obtained for modeleyes having different corneal asphericities in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 7C depicts graphically simulated MTF at 100 lp/mm obtained formodel eyes having different corneal asphericities in which an IOL isincorporated, as a function of the IOL's shape factor,

FIG. 8A depicts simulated spherical aberration exhibited by two modeleyes characterized by different corneal radii as a function of the shapefactor of an IOL incorporated in the models,

FIG. 8B depicts simulated MTF at 50 lp/mm exhibited by two model eyescharacterized by different corneal radii as a function of the shapefactor of an IOL incorporated in the models,

FIG. 8C depicts simulated MTF at 100 lp/mm exhibited by two model eyescharacterized by different corneal radii as a function of the shapefactor of an IOL incorporated in the models,

FIG. 9A depicts simulated spherical aberration exhibited by a pluralityof model eyes having different axial lengths as a function of the shapefactor of an IOL incorporated in the models,

FIG. 9B depicts simulated MTFs at 50 lp/mm exhibited by a plurality ofmodel eyes having different axial lengths as a function of the shapefactor of an IOL incorporated in the models,

FIG. 9C depicts simulated MTFs at 100 lp/mm exhibited by a plurality ofmodel eyes having different axial lengths as a function of the shapefactor of an IOL incorporated in the models,

FIG. 10 is a schematic side view of a lens according to one embodimentof the invention having an aspheric anterior surface,

FIG. 11 presents a plurality of graphs depicting the sag of an asphericsurface of two lenses in accordance with the teachings of the inventionhaving different shape factors, and

FIG. 12 graphically presents Monte Carlo simulation results for opticalperformance of a plurality of IOLs as a function of manufacturingtolerances.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 schematically depicts an IOL 10 in accordance with one embodimentof the invention having an optic 12 that includes an anterior surface 14and a posterior surface 16. In this embodiment, the anterior andposterior surfaces 14 and 16 are symmetrically disposed about an opticalaxis 18, though in other embodiments one or both of those surfaces canexhibit a degree of asymmetry relative to the optical axis. Theexemplary IOL 10 further includes radially extending fixation members orhaptics 20 that facilitate its placement in the eye. In this embodiment,the optic is formed of a soft acrylic polymer, commonly known asAcrysof, though in other embodiments, it can be formed of otherbiocompatible materials, such as silicone or hydrogel. The lens 10provides a refractive optical power in a range of about 6 to about 34Diopters (D), and preferably in a range of about 16 D to about 25 D.

In this exemplary embodiment, the lens 10 has a shape factor in a rangeof about 0 to about 2. More generally, in many embodiments, the shapefactor of the lens 10 can range from about −0.5 to about 4. As known inthe art, the shape factor of the lens 10 can be defined in accordancewith the following relation: $\begin{matrix}{{{Shape}\quad{{Factor}(X)}} = \frac{C_{1} + C_{2}}{C_{1} - C_{2}}} & {{Eq}.\quad(1)}\end{matrix}$wherein C₁ and C₂ denote, respectively, the curvatures of the anteriorand posterior surfaces.

The shape factor of the IOL 10 can affect the aberrations (e.g.,spherical and/or astigmatic aberrations) that the lens can introduce asa result of its tilt and decentration, e.g., when implanted in thesubject's eye or in a model eye. As discussed in more detail below,aberrations caused by a plurality of IOLs with different shape factorswere theoretically studied as a function of tilt and decentration byutilizing a model eye. Those studies indicate that IOLs having a shapefactor in a range of about 0 to about 2 introduce much reducedaberrations as a result of tilt and decentration.

More particularly, to study the effects of an IOL's shape factor onaberrations induced by its tilt and decentration, a hypothetical eyemodel having optical properties (e.g., corneal shape) similar to thoseof an average human eye was employed. The radii of optical surfaces andthe separations between optical components were chosen to correspond tomean values of those parameters for the human population. The refractiveindices of the optical components were chosen to provide selectedrefractive power and chromatic aberrations. Further, the anteriorcorneal surface of the model was selected to have an ashperical shape.An IOL under study replaced the natural lens in the model. Table 1 belowlists the various design parameters of the model eye: TABLE 1 Thick-Dia- Radius ness meter Conic Surface Type (mm) (mm) Class (mm) ConstantOBJ Standard Infinity Infinity 0.000 0.000 1 Standard Infinity 10.0005.000 0.000 2 Standard 7.720 0.550 Cornea 14.800 −0.260 3 Standard 6.5003.050 Aqueous 12.000 0.000 STO Standard Infinity 0.000 Aqueous 10.0000.000 5 Standard 10.200 4.000 Lens 11.200 −3.132 6 Standard −6.00016.179 Vitreous 11.200 −1.000 IMA Standard −12.000 24.000 0.000

An optical design software marketed as Zemax® (version Mar. 4, 2003,Zemax Development Corporation, San Diego, Calif.) was utilized for thesimulations of the optical properties of the model eye. A merit functionwas defined based on the root-mean-square (RMS) wavefront aberration,that is, the RMS wavefront deviation of an optical system from a planewave. In general, the larger the RMS wavefront error, the poorer is theperformance of the optical system. An optical system with an RMSwavefront error that is less than about 0.071 waves is typicallyconsidered as exhibiting a diffraction-limited optical performance.

The effects of misalignment (tilt and/or decentration) of an IOL on itsoptical performance for a number of different shape factors wassimulated by placing the IOLs in the above model eye and utilizing theZemax® software. For these simulations, the IOL was assumed to havespherical surfaces so as to investigate the effects of the shape factoralone (as opposed to that of the combined shape factor and asphericity).To simulate the scotopic viewing conditions for old patients, a 5 mmentrance pupil was chosen. The following misalignment conditions wereconsidered: 1.5 mm IOL decentration and a 10-degree IOL tilt. These twoconditions represent the extreme cases of IOL misalignments.

FIG. 2 presents the simulated magnitude of different aberration types(spherical aberration, defocus, coma and astigmatism) as a function ofthe shape factor for 1.5 mm decentration of the IOL. These simulationsindicate that IOLs with a shape factor in a range of about 0 to about 2exhibit much lower aberrations as a result of the decentration. Forexample, an IOL with a shape factor of about 1 introduces a defocusaberration of 0.07 D compared to a defocus aberration of 0.32 Dintroduced by an IOL having a shape factor of −1.

FIG. 3 presents the simulation results for aberrations introduced as aresult of the IOL's tilt. These results indicate that the defocus andastigmatic aberrations are not significantly influenced by the IOL'sshape factor while the coma and spherical aberrations exhibit evenstronger dependence on the shape factor than their dependence in case ofthe IOL's decentration. Again, the IOLs with shape factors in a range ofabout 0 to 2 exhibit a stable performance.

In other aspects, it has been discovered that certain biometricparameters of the eye (e.g., corneal radius and axial length) can beconsidered while selecting the shape factor of an IOL for implantationin the eye to provide enhanced performance of the lens. As discussed inmore detail below, in some embodiments, optimal IOL shape factors areprovided for different eye populations, e.g., average human eye (eyeswith average values for certain biometric parameters), and otherpopulations characterized by extreme values for those parameters.

The biometric parameters of the above eye model were varied to simulatethe performance of a plurality of IOLs having different shape factorsfor different eyes. For an average human eye, a corneal radius (r) of7.72 mm, a corneal asphericity (Q) of −0.26, an anterior chamber depth(ACD) of 4.9 mm, and an axial length (AL) of 24.4 mm were assumed. Toinvestigate human eyes with extreme large or small biometric values, theanterior chamber depth was varied from 4.3 mm to 5.5 mm, the cornealasphericity was varied from −0.50 to 0, the corneal radius was variedfrom 7.10 mm to 8.60 mm, and the axial length was varied from 22.0 mm to26.0 mm. These ranges are sufficiently broad to cover the valuesexhibited by the majority of the population. The optical performance ofthe IOLs was evaluated based on two criteria: calculated wave aberrationand modulation transfer function (MTF). As known to those havingordinary skill in the art, the MTF provides a quantitative measure ofimage contrast exhibited by an optical system, e.g., a system formed ofan IOL and the cornea. More specifically, the MTF of an imaging systemcan be defined as a ratio of a contrast associated with an image of anobject formed by the optical system relative to a contrast associatedwith the object.

Table 2 below presents the simulation results of the optical performanceof IOLs having shape factors in a range of about −2 to about 4 for aneye having an average anterior chamber depth (ACD) of 4.9 mm, a cornealradius of 7.72 mm, a corneal asphericity of −0.26, and an axial length(AL) of 24.4 mm, at a pupil size of 5 mm. TABLE 2 Shape Spherical Factor(X) Aberration (SA) MTF at 50 lp/mm MTF at 100 lp/mm −2 0.478 0.0370.095 −1.5 0.386 0.117 0.051 −1 0.307 0.212 0.011 −0.5 0.244 0.331 0.0160 0.195 0.455 0.128 0.5 0.162 0.555 0.250 1 0.142 0.615 0.334 1.5 0.1340.637 0.366 2 0.138 0.625 0.348 3 0.174 0.516 0.199 4 0.239 0.340 0.021

For graphical presentation of the information in Table 2, FIGS. 4A and4B provide, respectively, the calculated spherical aberration and MTFpresented in Table 1 as a function of IOL's shape factor.

Table 3 below presents the simulation results for the opticalperformance of a plurality of IOLs having shape factors in the aboverange of −2 to 4 at a pupil size of 5 mm for an eye having a smallanterior chamber depth (ACD) of 4.3 mm, but the same corneal radius(7.72 mm) and asphericity (−0.26) as well as axial length (24.4 mm) asthat employed in the previous simulation. FIGS. 5A and 5B graphicallydepict, respectively, the calculated spherical aberration (SA) and theMTF presented in Table 3 as a function of the IOL's shape factor. TABLE3 Shape Sph. Aberration Factor (X) (waves) MTF at 50 lp/mm MTF at 100lp/mm −2 0.461 0.047 0.095 −1.5 0.374 0.125 0.042 −1 0.300 0.219 0.014−0.5 0.240 0.337 0.021 0 0.194 0.457 0.130 0.5 0.161 0.553 0.249 1 0.1410.613 0.331 1.5 0.133 0.636 0.365 2 0.136 0.627 0.353

Table 4 below presents the simulation results for the opticalperformance of a plurality of IOLs having shape factors in the aboverange of −2 to 4 at a pupil size of 5 mm for an eye having a largeanterior chamber depth (ACD) of 5.5 mm, a corneal radius of 7.72 mm, acorneal asphericity of −0.26 and an axial length of 24.4 mm. Further,FIGS. 6A and 6B graphically depict, respectively, the calculatedspherical aberration (SA) and the MTF presented in Table 4 as a functionof the IOL's shape factor. TABLE 4 Shape Sph. Aberration Factor (X)(waves) MTF at 50 lp/mm MTF at 100 lp/mm −2 0.498 0.026 0.093 −1.5 0.3990.108 0.059 −1 0.316 0.204 0.008 −0.5 0.249 0.325 0.011 0 0.198 0.4540.125 0.5 0.162 0.556 0.251 1 0.142 0.617 0.336 1.5 0.135 0.637 0.365 20.140 0.622 0.342

These simulations indicate that IOLs with shape factors in a range ofabout −0.5 to about 4, and particularly those having shape factors in arange of about 0 to about 2, provide enhanced optical performance. Thesimulations, however, show that anterior chamber depth does notsignificantly affect the performance of an IOL.

Although in the afore-mentioned simulations the spherical aberrationswere considered, in the IOL is misaligned relative to the cornea, otheraberrations (e.g., defocus, astigmatism and coma) can also be present.The simulations of these aberrations for average, small and large ACDconfirm that the aberrations can be minimized by utilizing shape factorsin a range about 0 to about 2.

The impact of corneal asphericity (Q) on optimal IOL shape factor wasalso investigated by utilizing the aforementioned eye model andcalculating spherical aberration and MTF for Q-=0 (spherical), Q=−0.26and Q=−0.50. The more negative the Q value, the flatter is theperipheral portion of the cornea. Q=−0.26 corresponds to the asphericityof the normal human cornea while Q=−0.50 corresponds to the asphericityof an extremely flat cornea. Table 5 below lists the results of thesesimulations, with FIGS. 7A, 7B and 7C graphically depicting,respectively, the simulated spherical aberration, the MTF at 50 lp/mmand the MTF at 100 lp/mm as a function of the IOL's shape factor. TABLE5 SA (micron) MTF@501 p/mm MTF@1001 p/mm X Q = 0 Q = −0.26 Q = −0.50 Q =0 Q = −0.26 Q = −50 Q = 0 Q = −0.26 Q = −0.50 −2 0.609 0.478 0.364 0.0000.037 0.143 0.036 0.095 0.027 −1.5 0.524 0.386 0.264 0.010 0.117 0.2920.084 0.051 0.007 −1 0.451 0.307 0.180 0.058 0.212 0.503 0.091 0.0110.182 −0.5 0.392 0.244 0.112 0.111 0.331 0.702 0.057 0.016 0.463 0 0.3470.195 0.061 0.159 0.455 0.822 0.016 0.128 0.661 0.5 0.315 0.162 0.0250.200 0.555 0.869 0.007 0.250 0.742 1 0.295 0.142 0.005 0.230 0.6150.879 0.012 0.334 0.759 1.5 0.288 0.134 0.002 0.243 0.637 0.879 0.0120.366 0.759 2 0.29 0.138 0.003 0.238 0.625 0.879 0.013 0.348 0.759 30.321 0.174 0.045 0.189 0.516 0.848 0.004 0.199 0.704 4 0.378 0.2390.117 0.120 0.340 0.688 0.046 0.021 0.443

The spherical aberration exhibited by a spherical cornea (Q=0) issignificantly larger than those exhibited by the aspherical corneas(Q=−0.26 and Q=−0.50), as expected. As a result, the MTFs associatedwith Q=0 are lower than those for Q=−0.26 and Q=−0.50. However, for eachof the three cases, the above simulations indicate that an optimal IOLshape factor lies in a range of about −0.5 to about 4, and preferably ina range of about 0 to about 2.

In another set of simulations, the effect of corneal radius on optimalshape factor was investigated. Table 6 below presents the simulationresults corresponding to spherical aberration as well as MTFs at 50lp/mm and 100 lp/mm obtained for a plurality of IOLs having shapefactors in a range of about −2 to about 8 by utilizing theafore-mentioned eye model and varying the corneal radius. Morespecifically, the ACD, Q and AL were fixed, respectively, at 4.9 mm,−0.26, and 24.4 mm while the corneal radius was varied. FIGS. 8A, 8B and8C graphically depict, respectively, variations of the sphericalaberration, the MTF at 50 lp/mm and the MTF at 100 lp/mm in thesesimulations as a function of the IOL's shape factor for two differentradii. TABLE 6 r SA (waves) MTF@501 p/mm MTF@1001 p/mm r = 7.10 r = 7.72r = 8.60 r = 7.10 r = 7.72 r = 8.60 r = 7.10 r = 7.72 r = 8.60 X mm mmmm mm mm mm mm mm mm −2 0.312 0.478 0.856 0.196 0.037 0.086 0.010 0.0950.031 −1.5 0.282 0.386 0.635 0.245 0.117 0.00 0.015 0.051 0.032 −1 0.2550.307 0.447 0.297 0.212 0.07 0.002 0.011 0.086 −0.5 0.233 0.244 0.3000.347 0.331 0.234 0.029 0.016 0.011 0 0.215 0.195 0.195 0.393 0.4550.468 0.067 0.128 0.139 0.5 0.201 0.162 0.133 0.432 0.555 0.65 0.1050.250 0.382 1 0.190 0.142 0.111 0.463 0.615 0.711 0.139 0.334 0.476 1.50.182 0.134 0.127 0.485 0.637 0.667 0.165 0.366 0.408 2 0.177 0.1380.174 0.499 0.625 0.528 0.182 0.348 0.210 3 0.175 0.174 0.344 0.5030.516 0.173 0.188 0.199 0.008 4 0.182 0.239 0.579 0.483 0.340 0.0080.163 0.021 0.062 5 0.195 — — 0.444 — — 0.118 — — 6 0.213 — — 0.394 — —0.067 — — 7 0.234 — — 0.339 — — 0.022 — — 8 0.258 — — 0.285 — — 0.007 ——

These simulations indicate that for a very steep cornea (e.g., a cornealradius of 7.1 mm), the IOL's shape factor has a relatively small impacton the spherical aberration and the MTF. For example, in such a case,for shape factors in a wide range of about −1 to about 8, good opticalperformance is observed, though shape factors in a range of about 0.5 toabout 4 are preferred. However, for a cornea having a large radius,e.g., a radius larger than about 8.6 mm, an optimal range of about 0 toabout 2 (e.g., about 0.5 to about 2) for the IOL's shape factor isobserved. The peak of the IOL's optical performance as a function of theshape factor also shifts as the corneal radius varies from a small valueto a large one. For example, the simulations indicate a peak performanceat a shape factor of about 3 for a cornea with a radius of about 7.1 mmand at a shape factor of about 1 for a cornea with a radius of about 8.6mm.

Similar to corneal radius, it was discovered that an optimal shapefactor for an IOL can vary as a function of the eye's axial length. Byway of example, Table 7 below presents the results of simulations foroptical performance of a plurality of IOLs having shape factors in arange of −2 to 8 for a plurality of different axial lengths (ALs). Themodel eye utilized for these simulations was characterized by an ACD=4.9mm, a corneal radius (r)=7.72 mm, and a corneal asphericity (Q)=−0.26.The graphical representation of these simulations are provided in FIGS.9A, 9B and 9C for spherical aberration, MTF at 50 lp/mm and MTF at 100lp/mm, respectively. TABLE 7 SA (micron) MTF@501 p/mm MTF@1001 p/mm AL =22.0 AL = 24.4 AL = 26.0 AL = 22.0 AL = 24.4 AL = 26.0 AL = 22.0 AL =24.4 AL = 26.0 X mm mm mm mm mm mm mm mm mm −2 — 0.478 0.285 — 0.0370.209 — 0.095 0.021 −1.5 — 0.386 — — 0.117 — — 0.051 — −1 0.609 0.3070.215 0.000 0.212 0.364 0.078 0.011 0.047 −0.5 — 0.244 — — 0.331 — —0.016 — 0 0.281 0.195 0.166 0.322 0.455 0.507 0.015 0.128 0.200 0.5 —0.162 — — 0.555 — — 0.250 — 1 0.168 0.142 0.138 0.591 0.615 0.596 0.2840.334 0.318 1.5 — 0.134 — — 0.637 — — 0.366 — 2 0.240 0.138 0.127 0.4070.625 0.629 0.070 0.348 — 3 0.441 0.174 0.132 0.122 0.516 0.616 0.0540.199 0.345 4 0.718 0.239 0.147 0.011 0.340 0.565 0.030 0.021 0.275 5 —— 0.171 — — 0.488 — — 0.176 6 — — 0.202 — — 0.395 — — 0.075 7 — — 0.237— — 0.302 — — 0.001 8 — — 0.274 — — 0.222 — — 0.024

The above simulations indicate that while for a long axial length (e.g.,an axial length of about 26 mm), IOLs having shape factors over a widerange (e.g., in a range of about −1 to about 8) provide substantiallysimilar performance, for a short axial length (e.g., an axial length ofabout 22 mm), an optimal IOL shape factor lies in a range of about 0 toabout 2 (preferably in a range of about 0.5 to about 2). Further, thepeak of optical performance exhibits a shift as a function of axiallength variation.

In some embodiments, an anterior or a posterior surface of the IOLincludes an aspherical base profile selected to compensate for thecorneal spherical aberration. Alternatively, both anterior and posteriorsurfaces can be aspherical so as to collectively provide a selecteddegree of compensation for the corneal spherical aberration. By way ofexample, FIG. 10 shows an IOL 22 according to one embodiment of theinvention that includes an optic having a spherical posterior surface 24and an aspherical anterior surface 26. More specifically, the anteriorsurface 26 is characterized by a base profile that is substantiallycoincident with a putative spherical profile 26 a (shown by dashedlines) for small radial distances from an optical axis 28 but deviatesfrom that spherical profile as the radial distance from the optical axisincreases. In this embodiment, the aspherical anterior surface can becharacterized by the following relation: $\begin{matrix}{z = \frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}}} & {{Eq}.\quad(2)}\end{matrix}$wherein,

c denotes the curvature of the surface at its apex (at its intersectionwith the optical axis),

r denotes the radial distance from the optical axis, and

k denotes the conic constant.

In some embodiments, the conic constant k can range from about −1162 toabout −19 (e.g., from about −73 to about −27) and the shape factor ofthe lens can range from about −0.5 to about 4, and more preferably, fromabout 0 to about 2. To show the efficacy of such aspherical IOLs inreducing the corneal spherical aberrations, two aspherical IOLs weretheoretically designed. The IOLs were assumed to be formed of an acrylicpolymer commonly known as Acrysof. One of the IOLs was selected to havea shape factor of zero (X=0) while the other was chosen to have a shapefactor of 1 (X=1). The edge thickness for each IOL was fixed at 0.21 mm.For the IOL with X=0, the anterior and posterior radii were set,respectively, at 22.934 mm and −22.934 mm, the central thickness was setat 0.577 mm and the anterior surface asphericity (i.e., the conicconstant) was selected to be −43.656. For the IOL with X=1, theposterior surface was selected to be flat while the radius of theanterior surface was set at 11.785 mm. The central thickness of thislens was 0.577 mm and the anterior surface was assumed to have anasphericity characterized by a conic constant of −3.594. FIG. 11 showsthe sag of the anterior surfaces of these exemplary IOLs as a functionof radial distance from the optical axis.

The simulations of the optical performances of these two IOL designs inthe aforementioned eye model show a reduction of the total RMS wavefronterrors to about 0.000841 waves in case of the IOL having a shape factorthat approaches zero and to about 0.000046 in case of the IOL having ashape factor of unity.

Another factor that can affect the optical performance of an IOL is itseffective position. The effective lens position (e.g., defined here asthe location of the principal plane relative to the posterior surface)can vary as a function of the lens's shape. The location of the secondprincipal plane (PP₂) relative to the apex of the posterior surface canbe defined by the following relation: $\begin{matrix}{{PP}_{2} = \frac{{- n_{1}}{dF}_{1}}{n_{2}F_{L}}} & {{Eq}.\quad(3)}\end{matrix}$wherein n₁ and n₂ denote, respectively, the refractive indices of theIOL and the surrounding medium, F₁ represents the optical power of theanterior surface and F₂ represents the optical power of the lens, and dis the lens's central thickness. The haptics plane (the anchor plane forthe implanted IOL) located at the central-line of the lens edge can havea distance from the apex of the posterior surface specified as:$\begin{matrix}{{HL} = {{Sag}_{2} + \frac{ET}{2}}} & {{Eq}.\quad(4)}\end{matrix}$wherein ET denotes the lens's edge thickness and Sag₂ denotes the sagheight of the posterior surface at the lens's edge. Utilizing the aboveEquations (3) and (4), the location of the second principal pointrelative to the haptics plane can be defined as follows: $\begin{matrix}{{\Delta\quad{PP}_{2}} = {{Sag}_{2} + \frac{ET}{2} - \frac{n_{1}{dF}_{1}}{n_{2}F_{L}}}} & {{Eq}.\quad(5)}\end{matrix}$wherein ΔPP₂ denotes an offset shift of the principal plane, and theother parameters are defined above.

By way of example, the 2^(nd) principal plane shift for theaforementioned IOL having a shape factor of zero (X=0) was calculated(by utilizing the above equations) across a power range of 0 to about 35D as +/−0.03 mm, while the corresponding shift for the IOL having ashape factor of unity (X=1) was calculated as +/−0.15 mm.

To better appreciate the enhanced optical performance provided by theIOLs of the invention, some of the major factors contributing to thevariability of post-operative refractive errors can be considered. Thesefactors are generally classified into three categories: biometric dataerrors (ΔBiometric), IOL power errors (ΔIOLPower) and high-orderaberration contributions (ΔAberration). An overall variability (Rx) canbe calculated based on these factors by utilizing, e.g., the followingrelation: $\begin{matrix}{{RxError} = \sqrt{{\Delta\quad{Biometric}^{2}} + {\Delta\quad{IOLPower}^{2}} + {\Delta\quad{Aberration}^{2}}}} & {{Eq}.\quad(6)}\end{matrix}$

The ΔBiometric can, in turn, be defined in accordance with the followingrelation:ΔBiometric=√{square root over (Δk ² +ΔAL ² +ΔACD ²)}  Eq. (7)wherein Δk denotes the error in keratometric measurement, ΔAL denotesthe error in axial length measurement, and ΔACD denotes the error in theanterior chamber depth measurement. The ΔIOLPower can be defined inaccordance with the following relation:ΔIOLPower=√{square root over (ΔIOLStep² +ΔIOLTol² +ΔELP ²)}  Eq. (8)wherein ΔIOLStep denotes the variability caused by the use of IOLs whoseoptical powers differ by finite steps for correcting patients'refractive errors that vary over a continuous range, ΔIOLTol denotesmanufacturing power tolerance, and ΔELP denotes the variability in theshift of the IOL effective position across the power range. Further,ΔAberration can be defined in accordance with the following relation:ΔAberration=√{square root over (ΔAstig² +ΔSA ²+ΔOther²)}  Eq. (9)wherein ΔAstig, ΔSA, ΔOther denote, respectively, astigmatic, sphericaland other higher order aberrations.

The optical performance of the aforementioned exemplary IOL designshaving shape factors (X) of zero and unity were evaluated based onestimated Rx variability for three conditions: (1) uncorrected visualacuity (i.e., in the absence of corrective spectacles) with IOL powerstep of 0.5 D (UCVA), (2) uncorrected visual acuity with a refined IOLpower step of 0.25 D (UCVA+) and (3) best corrected visual acuity (i.e.,utilizing optimal corrective spectacles) (BCVA). The variability due tobiometric measurements was estimated from information available in theliterature. The focus of the analysis relates to estimatingcontributions of the spherical aberration, errors due to IOLmisalignments, and the 2^(nd) principal plane (PPL) shifts. Forcomparison purposes, a baseline value of 0.65 D was assumed for UCVA andUCVA+ and a baseline value of 0.33 D was assumed for BCVA, for eyes withspherical IOLs. Table 8 below lists absolute and percentage reductionsin Rx relative to the baseline values for the two IOLs: TABLE 8 IOL withX = 0 IOL with X = 1 UCVA −0.03 D −4.39%   0.00 D 0.45% UCVA+ −0.05 D−7.13% −0.01 D −2.16% BCVA −0.03 D −8.53% −0.05 D −13.87%

The information presented in Table 8 shows that reductions in Rxvariability are achieved for both IOLs (X=0, and X=1), thus indicatingimproved optical performance of those lenses. For the IOL with avanishing shape factor (X=0), the visual benefits are almost evenlydistributed among UCVA, UCVA+ and BCVA while for the other IOL (X=1),the visual benefit associated with BCVA is more pronounced.

A variety of known manufacturing techniques can be employed to fabricatethe lenses of the invention. The manufacturing tolerances can alsoaffect the optical performance of an IOL. By way of example, suchtolerances can correspond to variations of, e.g., surface radii, conicconstant, surface decentration, surface tilt, and surface irregularity,with tolerances associated with surface asphericity (conic constant)generally playing a more important role that others in affecting opticalperformance. Simulations, however, indicate that the IOL's misalignmentsupon implantation in the eye are typically more significant factors indegrading optical performance than manufacturing tolerances (e.g.,manufacturing errors can be nearly 10 times less than misalignmenterrors). By way of further illustration, the optical performance of theaforementioned aspherical lenses with X=0 and X=1, implanted in theaforementioned eye model, was theoretically investigated by employingMonte Carlo simulations. More specifically, 500 hypothetical lenses weregenerated under constraints of typical manufacturing tolerances and wererandomly oriented relative to the cornea. For example, the tolerancesassociated with the surface radii, surface irregularities, and surfacedecentration and tilt were assumed to be, respectively, within +/−0.1mm, 2 fringes, 0.05 mm and 0.5 degrees. The results of the Monte Carlosimulations are summarized in FIG. 12. More than 50% of the simulatedeyes exhibit an RMS wavefront error that is less than about 0.2 waves(about 0.08 D equivalent defocus). For the lens having X=1, about 98% ofthe simulated eyes show a wavefront error less than about 0.3 waves(about 0.12 D).

Those having ordinary skill in the art will appreciate that variouschanges can be made to the above embodiments without departing from thescope of the invention.

1. An ophthalmic lens, comprising an optic having an anterior surfaceand a posterior surface, said optic exhibiting a shape factor in a rangeof about −0.5 to about
 4. 2. The ophthalmic lens of claim 1, whereinsaid optic exhibits a shape factor in a range of about 0 to about
 2. 3.The ophthalmic lens of claim 1, wherein said optic comprises abiocompatible polymeric material.
 4. The ophthalmic lens of claim 3,wherein the polymeric material is selected from the group consisting ofacrylic, silicone and hydrogel materials.
 5. The ophthalmic lens ofclaim 1, wherein both of said surfaces have a generally convex profile.6. The ophthalmic lens of claim 1, wherein one of said surfaces has agenerally convex profile and the other surface has a substantially flatprofile.
 7. The ophthalmic lens of claim 1, wherein one of said surfaceshas a generally concave profile and the other surface has asubstantially flat profile.
 8. The ophthalmic lens of claim 1, whereinone of said surfaces has a generally concave profile and the othersurface has a generally convex profile.
 9. The ophthalmic lens of claim1, wherein at least one of said surfaces is characterized by anaspherical base profile.
 10. The ophthalmic lens of claim 9, whereinsaid aspheric base profile is characterized by a conic constant (Q) in arange of about −73 to about −27.
 11. The ophthalmic lens of claim 1,wherein said lens comprises an intraocular lens.
 12. An ophthalmic lens,comprising an optic having an anterior surface and a posterior surface,at least one of said surfaces being characterized by an aspherical baseprofile defined by the following relation:$z = \frac{c\quad r^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}}$wherein, c denotes the curvature of the surface at its apex (at itsintersection with the optical axis), r denotes the radial distance fromthe optical axis, and k denotes the conic constant, wherein c is in arange of about 0.0152 mm⁻¹ to about 0.0659 mm⁻¹, r is in a range ofabout 0 to about 5 mm, and k is in a range of about −73 to about −27,wherein said optic exhibits a shape factor in a range of about −0.5 toabout
 4. 13. The ophthalmic lens of claim 12, wherein said opticexhibits a shape factor in a range of about 0 to about
 2. 14. Theophthalmic lens of claim 12, wherein said lens comprises an intraocularlens.
 15. The ophthalmic lens of claim 12, wherein said surfacescooperatively provide a refractive optical power in a range of about 16D to about 25 D.
 16. The ophthalmic lens of claim 12, wherein said opticis formed of a biocompatible polymeric material.
 17. An intraocular lensadapted for implantation in an eye having a corneal radius equal to orless than about 7.1 mm, comprising an optic having an anterior surfaceand a posterior surface, said optic exhibiting a shape factor in a rangeof about −0.5 to about
 4. 18. The intraocular lens of claim 17, whereinoptic exhibits a shape factor in a range of about +0.5 to about
 4. 19.The intraocular lens of claim 17, wherein said optic exhibits a shapefactor in a range of about 1 to about
 3. 20. An intraocular lens adaptedfor implantation in an eye having a corneal radius in a range of about7.1 to about 8.6 mm, comprising an optic having an anterior surface anda posterior surface, said optic exhibiting a shape factor in a range ofabout 0 to about
 3. 21. The intraocular lens of claim 20, wherein saidoptic exhibits a shape factor in a range of about +0.5 to about
 3. 22.The intraocular lens of claim 20, wherein said optic exhibits a shapefactor in a range of about 1 to about
 2. 23. An intraocular lens adaptedfor implantation in an eye having a corneal radius equal to or greaterthan about 8.6 mm, comprising an optic having an anterior surface and aposterior surface, said optic exhibiting a shape factor in a range ofabout +0.5 to about
 2. 24. The intraocular lens of claim 23, whereinsaid optic exhibits a shape factor in a range of about 1 to about
 2. 25.An intraocular lens adapted for implantation in an eye having an axiallength equal to or less than about 22 mm, comprising an optic having ananterior surface and a posterior surface, said optic having a shapefactor in a range of about 0 to about
 2. 26. The intraocular lens ofclaim 25, wherein the optic exhibits a shape factor in a range of about0.5 to about
 2. 27. An ophthalmic lens, comprising an optic having ananterior surface and a posterior surface, at least one of said surfaceshaving an aspherical profile characterized by a conic constant in arange of about −73 to about −27, wherein said optic exhibits a shapefactor in a range of about −0.5 to about
 4. 28. The ophthalmic lens ofclaim 27, wherein said aspherical profile is characterized by a conicconstant in a range of about −73 to about −27, and said optic exhibits ashape factor in a range of about 0 to about
 2. 29. A method ofcorrecting vision, comprising selecting an IOL comprising an opticexhibiting a shape factor in a range of about −0.5 to about 4 forimplantation in an eye having a corneal radius equal or less than about7.1 mm.
 30. The method of claim 29, wherein the shape factor of theoptic is selected to be in a range of about +0.5 to about
 4. 31. Amethod of correcting vision, comprising selecting an IOL comprising anoptic exhibiting a shape factor in a range of about 0 to about 3 forimplantation in an eye having a corneal radius in a range of about 7.1mm to about 8.6 mm.
 32. The method of claim 31, wherein the shape factorof the optic is selected to be in a range of about +0.5 to about
 3. 33.A method of correcting vision, comprising selecting an IOL comprising anoptic exhibiting a shape factor in a range of about 0.5 to about 2 forimplantation in an eye having a corneal radius equal to or greater thanabout 8.6 mm.
 34. A method of correcting vision, comprising selecting anIOL comprising an optic exhibiting a shape factor in a range of about 0to about 2 for implantation in an eye having an axial length equal to orless than about 22 mm.
 35. The method of claim 34, wherein a shapefactor of the optic is selected to be in a range of about 0.5 to about2.
 36. A method of designing an ophthalmic lens, comprising defining anerror function indicative of variability in performance of a lens in apatient population based on estimated variability in one or morebiometric parameters associated with that population, and selecting ashape factor for the lens that reduces said error function relative to areference value.
 37. The method of claim 36, wherein said error functionfurther incorporates an estimated error in optical power correctionprovided by the lens.
 38. The method of claim 37, wherein said errorfunction further incorporates an estimated aberration error.
 39. Themethod of claim 38, wherein said error function (RxError) is defined bythe following relation:${RxError} = \sqrt{{\Delta\quad{Biometric}^{2}} + {\Delta\quad{IOLPower}^{2}} + {\Delta\quad{Aberration}^{2}}}$wherein, ΔBiometric denotes variability due to biometric data errors,ΔIOLPower denotes variability due to optical power errors, andΔAberration denotes variability due to aberration contributions.
 40. Themethod of claim 39, wherein ΔBiometric is defined by the followingrelation:ΔBiometric=√{square root over (Δk ² +ΔAL ² +ΔACD ²)} wherein, Δk denoteserror in keratometric measurements, ΔAL denotes error in axial lengthmeasurements, and ΔACD denotes error in anterior chamber depthmeasurements.
 41. The method of claim 39, wherein ΔAberration is definedby the following relation:ΔAberration=√{square root over (ΔAstig² +ΔSA ²+ΔOther²)} wherein, ΔAstigrepresents variability due to astigmatic aberration, ΔSA representsvariability due to spherical aberration, and ΔOther representsvariability due to other aberrations.
 42. The method of claim 39,wherein ΔIOLPower is defined by the following relation:ΔIOLPower=√{square root over (ΔIOLStep² +ΔIOLTol² +ΔELP ²)} wherein,ΔIOLStep represents variability caused by difference between the lenspower and a power need of a patient, ΔIOLTol represents manufacturingpower tolerance, and ΔELP represents variability in a shift of the lenseffective position within the eye.